Efficient Maximum Fair Clique Search over Large Networks

Mining cohesive subgraphs in attributed graphs is an essential problem in the domain of graph data analysis. The integration of fairness considerations significantly fuels interest in models and algorithms for mining fairness-aware cohesive subgraphs. Notably, the relative fair clique emerges as a robust model, ensuring not only comprehensive attribute coverage but also greater flexibility in distributing attribute vertices. Motivated by the strength of this model, we for the first time pioneer an investigation into the identification of the maximum relative fair clique in large-scale graphs. We introduce a novel concept of colorful support, which serves as the foundation for two innovative graph reduction techniques. These techniques effectively narrow the graph's size by iteratively removing edges that do not belong to relative fair cliques. Furthermore, a series of upper bounds of the maximum relative fair clique size is proposed by incorporating consideration of vertex attributes and colors. The pruning techniques derived from these upper bounds can significantly trim unnecessary search space during the branch-and-bound procedure. Adding to this, we present a heuristic algorithm with a linear time complexity, employing both a degree-based greedy strategy and a colored degree-based greedy strategy to identify a larger relative fair clique. This heuristic algorithm can serve a dual purpose by aiding in branch pruning, thereby enhancing overall search efficiency. Extensive experiments conducted on six real-life datasets demonstrate the efficiency, scalability, and effectiveness of our algorithms

Characteristics of the impact pressure of debris flows

Debris flows are common geological hazards in mountainous regions worldwide. Predicting the impact pressure of debris flows is of major importance for hazard mitigation. Here, we experimentally investigate the impact characteristics of debris flows by varying the concentrations of debris grains and slurry. The measured impact pressure signal is decomposed into a stationary mean pressure (SMP) and a fluctuating pressure (FP) through empirical mode decomposition. The SMP of low frequency is caused by the thrusting of bulk flow while the FP of high frequency is induced by the collision of coarse debris grains, revealed by comparing the features of impact pressure spectra of pure slurries and debris flows. The peak SMP and the peak FP first increase and then decrease with the slurry density. The basal frictional resistance is reduced by the nonequilibrium pore-fluid pressure for debris flows with low-density slurry, which can increase the flow velocity and impact pressures. In contrast, the viscous flow of high-density slurry tends to reduce the flow velocity. The peak SMPs are well predicted by the Bernoulli equation and are related to the hydrostatic pressure and Froude number of the incident flow. The peak FPs depend on the kinetic energy and degree of segregation of coarse grains. The maximum degree of segregation occurs at an intermediate value of slurry density due to the transition of flow regime and fluid drag stresses. Our results facilitate predicting the impact pressures of debris flows based on their physical properties

Gold-Catalyzed Enantioselective Ring-Expanding Cycloisomerization of Cyclopropylidene Bearing 1,5-Enynes

An enantioselective ring-expanding cycloisomerization of 1,5-enynes bearing a cyclopropylidene moiety has been developed. This methodology provides a new approach to bicyclo[4.2.0]octanes, a structural motif present in many biologically active natural products